Editing Cronbach's alpha (section)

==Formula and calculation==
Cronbach's alpha is calculated by taking a score from each scale item and correlating it with the total score for each observation. The resulting correlations are then compared with the [[variance]] for all individual item scores. Cronbach's alpha is best understood as a function of the number of questions or items in a measure, the average [[covariance]] between pairs of items, and the overall variance of the total measured score.<ref>{{Cite web|last=Goforth|first=Chelsea|date=November 16, 2015|title=Using and Interpreting Cronbach's Alpha - University of Virginia Library Research Data Services + Sciences|url=https://data.library.virginia.edu/using-and-interpreting-cronbachs-alpha/|access-date=2022-09-06|website=University of Virginia Library|archive-date=2022-08-09|archive-url=https://web.archive.org/web/20220809031644/https://data.library.virginia.edu/using-and-interpreting-cronbachs-alpha/|url-status=live}}</ref><ref name=RM/>

<math display="block">\alpha = {k \over k-1 } \left(1 - {\sum_{i=1}^k \sigma^2_{y_i} \over \sigma^2_y} \right)</math>

where:

* <math>k</math> represents the number of items in the measure
* <math>\sigma_{y_i}^2</math> the variance associated with each item ''i''
* <math>\sigma_y^2</math> the variance associated with the total scores, <math>y = \sum_{i=1}^k y_i</math>

Alternatively, it can be calculated through the following formula:<ref>{{Cite AV media|title=Cronbach's Alpha (Simply explained)|url=https://www.youtube.com/watch?v=W9uPvAmtTOk&t=248|date=October 27, 2021|access-date=2023-08-01|author=DATAtab|publisher=YouTube|time=4:08}}</ref>
:<math> \alpha = {k \bar c \over \bar v + (k - 1) \bar c} </math>

where:

* <math>\bar v</math> represents the average variance
* <math>\bar c</math> represents the average inter-item covariance.